I found a baby pigeon in downtown Montreal, please help.

[LovelyFlight]

This morning I found a baby pigeon walking on St Catherine street near Alexis Nihon mall (Atwater). She cannot fly. From the little research I did online she looks to be about 18 days old. There was no nest around where I found her and there are a lot of cars and people.

I brought her home and fed her baby bird food in warm water, she ate about 40 ml already. She seems to know how to eat from the syringe (I was worried I would choke her, I have absolutely no experience with birds). She does not look injured but her feathers look a bit rare, although I don't know what she's supposed to look like...She pooped twice already, it looked like regular bird poop. I placed her in a big recycling box lined with an electric blanket and paper towels, and the box is in our spare bedroom, safely away from our two, very curious cats

I have to say that she is the cutest little thing, she is very vocal and full of energy and very affectionate. She climbs on my shoulder and rests under my cheek and pecks at my face

My questions are:

1. Is there anything else I should be doing right away?
2. How often should I feed her and how much?
3. It is getting very cold out there, I will not let her go until I know she is going to be perfectly fine; is there a sanctuary in Montreal where I could bring her so she could socialize with other pigeons?

Any help would be greatly appreciated, I will keep researching.

Thank you!